Answer:
Step-by-step explanation:
From the table attached,
x-intercept of the linear function is, the value of 'x' when f(x) = 0
x = 3 [x-intercept]
Function 'g' is the sum of 2 and the cube root of the sum of three time x and 1.
g(x) = ![2+\sqrt[3]{3x+1}](https://tex.z-dn.net/?f=2%2B%5Csqrt%5B3%5D%7B3x%2B1%7D)
For x-intercept,
g(x) = 0
![2+\sqrt[3]{3x+1}=0](https://tex.z-dn.net/?f=2%2B%5Csqrt%5B3%5D%7B3x%2B1%7D%3D0)
3x + 1 = (-2)³
3x + 1 = -8
3x = -8 - 1
3x = -9
x = -3
Therefore, the x-intercept of function 'f' is different or greater than the x-intercept of function g.
As for this problem, it would be best to approach this with a ratio to ratio approach. This would then involve the equation with fractions which is the common conversion from ratios to easily solve the problems concerning these. The equation then would look somehow like this:
0.01 miles / 1 hour = x miles / 2.4 hours
The easiest way would be just to multiply the numerator, which is the miles, to 2.4. So when it is multiplied to the numerator, the equation then would turn to:
0.01 miles x 2.4 / 1 hour = x miles / 2.4 hours
0.024 miles would be the answer.
Answer:
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
The value of p is 0 .00233. The result is significant at p < 0.10.
Step-by-step explanation:
1) Let the null and alternate hypothesis be
H0: μboys − μgirls > 0
against the claim
Ha: μboys − μgirls ≤ 0
2) The significance level is set at 0.01
3) The critical region is z ≤ ± 1.28
4) The test statistic
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
Here p1= 397/768= 0.5169 and p2= 331/745=0.4429
pc = 397+331/768+745
pc= 0.4811
qc= 1-pc= 1-0.4811=0.5188
5) Calculations
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
z= 0.5169-0.4429/√ 0.4811*0.5188( 1/768+ 1/745)
z= 2.82
6) Conclusion
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
7)
The value of p is 0 .00233. The result is significant at p < 0.10.
It can have however many x intercepts it wants,
<span>BUT, to be a function it must pass the vertical line test. </span>
<span>this means you have to look at the graph and see if a vertical line drawn anywhere hits the graph more than once. </span>
<span>if it hits it more than once, it is NOT a function.
</span>
An example is a polynomial function to the infinite degree. That is
f(x) = lim (n --> infinity) [ x^n]
but only 1 y intercept (vertical line test remember)
